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This Article Full Text Full Text (PDF) All Versions of this Article: 291/6/H2816    most recent 00135.2006v1 Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a friend Similar articles in this journal Similar articles in Web of Science Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Brown, D. R. Articles by Randall, D. C. Search for Related Content PubMed PubMed Citation Articles by Brown, D. R. Articles by Randall, D. C.

Empirical and theoretical analysis of the extremely low frequency arterial blood pressure power spectrum in unanesthetized rat

¹Center for Biomedical Engineering, Wenner-Gren Laboratory, University of Kentucky; ²Graduate Center for Nutritional Sciences, University of Kentucky; and ³Department of Physiology, University of Kentucky College of Medicine, Lexington, Kentucky

Submitted 6 February 2006 ; accepted in final form 7 July 2006

The slope of the log of power versus the log of frequency in the arterial blood pressure (BP) power spectrum is classically considered constant over the low-frequency range (i.e., "fractal" behavior), and is quantified by in the relationship "1/f." In practice, the fractal range cannot extend to indefinitely low frequencies, but factor(s) that terminate this behavior, and determine , are unclear. We present 1) data in rats (n = 8) that reveal an extremely low frequency spectral region (0.083–1 cycle/h), where approaches 0 (i.e., the "shoulder"); and 2) a model that 1) predicts realistic values of within that range of the spectrum that conforms to fractal dynamics (1–60 cycles/h), 2) offers an explanation for the shoulder, and 3) predicts that the "successive difference" in mean BP (mBP) is an important parameter of circulatory function. We recorded BP for up to 16 days. The absolute difference between successive mBP samples at 0.1 Hz (the successive difference, or ) was 1.87 ± 0.21 mmHg (means ± SD). We calculated for three frequency ranges: 1) 0.083–1; 2) 1–6; and 3) 6–60 cycles/h. The for all three regions differed (P < 0.01). For the two higher frequency ranges, indicated a fractal relationship (_6–60/h = 1.27 ± 0.01; _1–6/h = 1.80 ± 0.16). Conversely, the slope of the lowest frequency region (i.e., the shoulder) was nearly flat (_{0.083–1 /h} = 0.32 ± 0.28). We simulated the BP time series as a random walk about 100 mmHg with ranges above and below of 10, 30, and 50 mmHg and with from 0.5 to 2.5. The spectrum for the conditions mimicking actual BP time series (i.e., range, 85–115 mmHg; , 2.00) resembled the observed spectra, with in the lowest frequency range = 0.207 and fractal-like behavior in the two higher frequency ranges ( = 1.707 and 2.057). We suggest that the combined actions of mechanisms limiting the excursion of arterial BP produce the shoulder in the spectrum and that contributes to determining .

power spectra; circadian rhythm; computer model